Necessary and sufficient conditions for boundedness of commutators associated with Calderon-Zygmund operators on slice spaces

摘要

Let t is an element of (0, infinity) and r, p is an element of (1, infinity). In this paper, we establish new versions of the Fefferman-Stein inequality over the slice space (E-r(p))(t)(R-n), and further reobtain the boundedness of the Calderon-Zygmund operators with the standard kernel via a direct way rather than the extrapolation on slice spaces. Furthermore, we give two necessary and sufficient conditions for the boundedness of the commutator [b, T-Omega] generated by the locally integrable function b and the Calderon-Zygmund operator with the rough kernel T-Omega on slice spaces.

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